Question

The following quantum numbers are possible for how many orbitals $n = 3,l = 2,m = + 2?$
A. $1$
B. $2$
C. $3$
D. $4$

Answer 1

We know that in chemistry, every electron in any atom is represented by different quantum numbers which are namely as n, l, m all these terms have significance in contribution of the electron inside the atom. These numbers determine the orbital and spin of the electron.

Complete step by step answer:
Given information:
$n = 3$
$l = 2$
$m = + 2$
The term $n$ stands for principal quantum number. It specifies the energy of an electron and the size of the orbital. If an electron is higher than its $n$ number of shell level then it is said to be in excited state, if the electron lies in its configured shell number then it is said to be in ground state.
Here, the principal quantum number is, $n = 3$.
In chemistry, this principal quantum number has three allowed angular momentum denoted by $l$. Angular momentum quantum number is also the secondary Azimuthal number. It specifies the shape of an orbital of a given principal quantum number.
The angular momentum number is, $l = 2$. It has five orbitals.
The term $m$ stands for magnetic quantum number which specifies the orientation in space of an orbital of given energy $n$ and shape $l$.
For an atom with angular momentum $l = 2$, the magnetic quantum number ranges from $- 2{\text{ to + 2}}$.
Now, the orbital name of this configuration is $3d$ which a distinct orbital is. It can accommodate only two electrons. Hence, the given orbital is a single orbital and can allow only two electrons.
Hence,the correct option is option A.

Note:
We know that, in chemistry, the electronic configuration of any atom is determined by Aufbau principle. The building blocks of Aufbau principle are derived from the quantum number and the atomic orbitals. According to quantum theory, every electron is defined y wave function also called atomic orbital. This orbital defines the space where the electrons reside inside an atom. Energy changes within an atom as the electron changes its wave pattern. The different quantum numbers are the numeric representation of this theory and it is used to determine the space, shells, sub shells, orbitals and spin of an electron in an atom.